Transmission Characteristics and Inactivated Vaccine Effectiveness Against Transmission of SARS-CoV-2 Omicron BA.5 Variants in Urumqi, China

This cohort study investigates transmission characteristics and vaccine effectiveness against transmission of SARS-CoV-2 Omicron BA.5 variants in China.

• household contacts (i.e., household members regularly living within the same or close space, or relatives who had close contact with case) • workplace or school contacts (i.e., a work colleague or classmate), and • community contacts (i.e., healthcare-givers and patients in the same ward, persons sharing a vehicle or restaurant, and community workers having contact with case in public places). For those contacts who were (eventually) test-positive for COVID-19, we treated these contacts as infectee, and their source case (who were confirmed with COVID-19 in the first place) as infector. We extracted this epidemiologically linked infector and infectee in pairs, and collected their individual-based data for all these transmission pairs.
If it was unclear who was the source case (e.g., more than one infectors were linked to a close contact), this contact would be excluded from analysis. In our study, none of such situation occurs in the dataset. eFigure 1. Key Amino Acid Substitutions in Genetic Sequence Samples From 11 Individuals With COVID-19 Cases labeled as integer from 1 to 11 on the horizontal axis. The colors of text at the left-hand side represented the AA substitutions in NTD (green), RBD (blue), FP (brown), and HR1 (purple).

S3.1 Generation interval
Generation interval (GI) is defined as the mean duration between time of infection of a secondary infectee and the time of infection of its primary infector [3,4]. We included transmission pairs with known exposure time for infectors and infectees to estimate the GI. The generation interval together with the reproduction number governs the progression of an epidemic. We denoted as the generation interval (GI) of the th transmission pair, and we assumed the GI of the Omicron BA.5.2 followed a gamma distribution, denoted by ℎ(. ). The GI can change over the course of an outbreak due to sampling bias [5]. In particular, the observed GIs was more likely to be shorter during an exponential growth phase (infectees with more recent exposure to an infector are more likely to be identified) but tend to be longer during the exponential decay phase of the outbreak [5]. In our study, the transmission pairs were collected during a whole epidemic wave that covering both increasing and decreasing phase, and thus our GI estimates would not suffer from such bias. We also considered the right-truncation of the time interval [6][7][8] that is, the generation interval generated by each infector is truncated due to the PHSMs that could curb the transmission (e.g., contact tracing and case isolation). Thus, the truncation-adjusted distribution function was Here, the (. ) is the cumulative density function of ℎ(. ). The is the isolation delay (i.e., the time interval between the isolation and symptom onset) of the infector for the -th transmission pair. The likelihood functions with and without truncation adjusted are given by:

S3.2 The period from exposure to viral shedding
The period from exposure to viral shedding was defined as the time interval between exposure and the first appearance of viral shedding, which may be considered a proxy for latent period. To estimate the distribution of the period from exposure to viral shedding, we included cases with known exposure date and RT-PCR test-positive dates. As serial intensive RT-PCR testing were conducted for each confirmed case during the study period, we considered the time that the -th case start to shed viral genetic particles was bounded by the first test-positive date (denoted by ) and the last test-negative date (denoted by ) of that case. Therefore, the observed period from exposure to viral shedding was interval-censored, which needs to be corrected in the estimation [9]. We excluded cases with a prior to his/her exposure date, which possibly indicating recall bias. We assumed the period from exposure to viral shedding followed a gamma distribution. We denoted as the exposure date of th case, as the start date of viral shedding, and (. ) as the gamma distribution of the period from exposure to viral shedding. Then the interval-censored likelihood function is constructed as follow:

S3.3 Viral shedding period
Confirmed COVID-19 cases with known serial RT-PCR testing date were used to calculate the viral shedding period, which may be considered a proxy for infectious period. Considering the last date for the th case to shed viral genetic particles was also bounded between the last testpositive date (denoted by ) and the first test-negative date (denoted by ) after infection, the observed viral shedding period was doubly interval-censored [10,11]. All included cases had an later than . We assumed the viral shedding period was gamma distributed, denoted by (. ). Then. we constructed the doubly interval-censored likelihood function as follow:

S3.4 Incubation period
The incubation period is the duration between the exposure and symptoms onset. We only included symptomatic cases with known exposure date to estimate the incubation period. We denoted as the incubation period of the th case, and we assumed it followed a gamma distribution, denoted by (. ). The likelihood function is given by: A graph to show the relationship of GI, incubation period, period from exposure to viral shedding and viral shedding period in Figure S3.1 (see below).

S3.5 Parameter estimation
For each key time interval, the parameters of gamma distribution were estimated by using the Metropolis-Hastings algorithm, which is a Markov chain Monte Carlo (MCMC) method, with noninformative prior distributions. The marginal posterior distribution was obtained from 10 000 iterations, among which the first 5 000 samples were discarded as for burn-in. The convergence of each MCMC chain was checked by using the trace plot and Gelman-Rubin-Brooks convergence diagnostic [12]. The median and 95% credible intervals (CrI) were obtained from the converged posterior distributions of each parameter.

S3.6 Supplementary results
The estimations of the key time interval distributions were summarized in Table S3.1.
As for results, we found that the mean GI was shorter in household settings than in nonhousehold settings, which could be attributed to the depletion of susceptible people within household (i.e., a lower potential for observing a longer GI) [13]. The mean GI decreased after the implementation of the lockdown measures, implicitly suggesting that the PHSMs contribute to trimming down the infectiousness profiles of individual cases. An early modelling study indicated that a delay of case isolation was positively associated with the duration of the serial interval [14], a metrics that metric used as a proxy of GI, which means the GI could be shortened on the basis of how quickly fast cases were isolated. Therefore, the GI estimates should also be interpreted in the context of different settings, and our GI estimates would be more generalizable for settings that had the same public health capacity as Urumqi.

eAppendix 4. Epidemic Growth and Reproduction Number
The exponential growth (or decay) was frequently used to capture the pattern of epidemic curve [15,16]. We fitted the observed daily cumulative number of COVID-19 cases denoted by ) (t C to an exponential growth model to estimate the growth rate (γ).
Given the estimated growth rate and GI, we estimated the reproduction number ( R ) by using the formula as per [17]: where the function ) (⋅ M was the moment generation function (MGF) of the probability density function (PDF) of GI. For GI following a gamma distribution with parameters shape α and rate β , then the R can be simplified as follows:

eAppendix 5. Contact Matrix and Mean Number of Offspring Infections by Age of Individuals Spreading and Receiving Infection
We relied on contact tracing data to characterize the age-specific contact matrixes and "who acquired infections from whom" (WAIFW) matrixes [18] for the infected individuals and their close contacts. A contact matrix comprised infectors and all of their close contacts (including both testpositive and test-negative individuals), whereas a WAIFW matrix only contains infectors and their test-positive contacts.
All cases were classified into 16 age groups according to their ages (i.e., 0 to 4 years, 5 to 9 years, 10 to 14 years, 15 to 19 years, 20 to 24 years, 25 to 29 years, 30 to 34 years, 35 to 39 years, 40 to 44 years, 45 to 49 years, 50 to 54 years, 55 to 59 years, 60 to 64 years, 65 to 69 years, 70 to 74 years, 75 to 79 years, and 80 years or older), to generate the age-specific contact and WAIFW matrixes. In addition, the age-specific contact and WAIFW matrixes stratified by contact settings and epidemic period (i.e., before and after lock down) were also constructed (see Figure S5.1). The constructed contact matrixes were shown in Figure S5